

A197494


Decimal expansion of least x>0 having cos(x)=(cos(Pi*x/3))^2.


2



1, 5, 6, 6, 0, 2, 3, 6, 1, 3, 6, 2, 2, 2, 8, 9, 7, 0, 2, 3, 0, 3, 8, 2, 0, 8, 2, 3, 9, 4, 8, 9, 4, 6, 1, 1, 0, 5, 0, 0, 2, 3, 7, 1, 8, 4, 2, 4, 8, 4, 9, 7, 1, 8, 2, 1, 8, 6, 5, 9, 9, 3, 4, 1, 5, 9, 8, 6, 8, 2, 4, 0, 3, 9, 2, 3, 5, 2, 3, 3, 2, 6, 4, 2, 1, 9, 4, 2, 2, 7, 2, 3, 3, 1, 9, 9, 4, 8, 2
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OFFSET

1,2


COMMENTS

The Mathematica program includes a graph. See A197476 for a guide for the least x>0 satisfying cos(b*x)=(cos(c*x))^2 for selected b and c.


LINKS

Table of n, a(n) for n=1..99.


EXAMPLE

x=1.566023613622289702303820823948946110500...


MATHEMATICA

b = 1; c = Pi/3; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.5, 1.6}, WorkingPrecision > 110]
RealDigits[t] (* A197494 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2}]


CROSSREFS

Cf. A197476.
Sequence in context: A217177 A157339 A029944 * A334381 A153415 A154010
Adjacent sequences: A197491 A197492 A197493 * A197495 A197496 A197497


KEYWORD

nonn,cons


AUTHOR

Clark Kimberling, Oct 15 2011


STATUS

approved



